Free-space continuous-variable quantum key distribution of unidimensional Gaussian modulation using polarized coherent states in an urban environment

An experiment evaluating continuous-variable quantum key distribution (CV-QKD) in an urban environment free-space channel has been accomplished using a single homodyne detector. This is based on Gaussian modulation with coherent states in the polarization degree of freedom. We achieved a QKD distance at 460 m at a repetition rate of 10 kHz. The secure key rate is 0.152 kbps at the typical reconciliation efficiency of 0.95. The experimental setup of this scheme is simplified, and the barrier for implementation has been remarkably reduced compared to that for traditional symmetric modulation protocols, for example, the GG02 protocol proposed in F. Grosshans and P. Grangier [Phys. Rev. Lett. 88, 057902 (2002)]. The influence of the security key rate by asymmetric modulation is small for a relatively low channel loss condition in a free-space environment. This scheme is expected to have significance for future practical applications.

Figure 1

Entanglement-based description of unidimensional CV-QKD. Alice prepares a two-mode squeezed vacuum state, then measures mode $A$ using homodyne detection; then the remaining part, mode $B_0$, is sent through the channel. Bob's nonideal detector equals a PBS followed by an ideal detector.

Figure 2

(a) Sender's side of the free-space CV-QKD experimental setup for a unidimensional protocol. HWP: half-wave plate. EOM: electro-optical modulator. BE: $10\times$ beam expander. Lenses 1 and 4: $\mathrm{focus}=100\mathrm{mm}, \mathrm{diameter}=25\mathrm{mm}$. Lenses 2 and 3: $\mathrm{focus}=50\mathrm{mm}, \mathrm{diameter}=25\mathrm{mm}$. DAQ: data acquisition. (b) Receiver's side of the free-space CV-QKD experimental setup for a unidimensional protocol. HWP: half-wave plate. QWP: quarter-wave plate. Lens 5: $\mathrm{focus}=200\mathrm{mm}, \mathrm{diameter}=100\mathrm{mm}$ (uncoated). Lens 6: $\mathrm{focus}=60\mathrm{mm}, \mathrm{diameter}=50\mathrm{mm}$. Lens 7: $\mathrm{focus}=150\mathrm{mm}, \mathrm{diameter}=50\mathrm{mm}$. BS: beam splitter. PBS: polarized beam splitter. DAQ: data acquisition.

Figure 3

Beam profiles are recorded by a CCD camera after two output ports of a PBS, on Bob's side and at the lens focus: vertically polarized (left) and horizontally polarized (right). For convenience, the two beam profiles are displayed in one figure. The horizontal and vertical axes are the position of the beam, in units of micrometers. The diameters of the two beams are not exactly the same, as the CCD deviates from the lens focus in the two directions. The profiles are nearly Gaussian in both the $x$ and $y$ directions, but the shape changes with time.

Figure 4

The center of the horizontal ($X$) and vertical ($Y$) directions as a function of time of the beam at the transmission port of the PBS. Measurement time is 21 min. Black: peak position in the $x$ direction. Red: peak position in the $y$ direction. Green: the position of the intensity center in the $x$ direction. Blue: the position of the intensity center in the $y$ direction. The average jitter in both directions is approximately 200 $\mu \mathrm{m}$ (blue and green lines).

Figure 5

Relative positions of peak intensity of the beam spot. Jitters in both directions are close.

Figure 6

They key rate at different channel transmittances. Solid line: GG02; dashed line: unidimensional protocol. Main parameters: $V_M=165,\epsilon =0.0375,V_{P1}=1.0,V_e=0.0219,\eta =0.872$; bpp: bit per pulse.